A Coriolis flowmeter has conventionally been used as a flowmeter for directly measuring the mass flow rate. When a fluid flowing through piping makes a rotational motion, the fluid receives a Coriolis force, which is in proportion to the vector product of the velocity vector of the flow and the angular velocity vector of the rotation. The Coriolis flowmeter measures the mass flow rate of the fluid by detecting, by some method or other, an elastic deformation of the piping generated by this inertial force.
The Coriolis flowmeter is a direct type mass flowmeter, and is of a relatively high accuracy among mass flowmeters. The Coriolis flowmeter is being rapidly improved in terms of accuracy with the recent progress in the digital signal processing technique. Further, the Coriolis flowmeter is capable of performing measurement practically on almost all kinds of fluid including liquid, gas, slurry, and a mixture phase flow of solid, gas, and liquid. Even in the case of a bubbled flow, it allows accurate measurement of mass flow rate if the bubbles are minute and uniform. Further, the feature of the Coriolis flowmeter resides in that the Coriolis flowmeter has no exposed object in its pipeline or no mechanically movable portions, and provides high maintainability. Further, the Coriolis flowmeter is a composite measuring instrument allowing simultaneous measurement of volume flow rate, density viscosity, and temperature, and has such a feature that it is basically free from the influence of the density, viscosity, etc. Thus, the Coriolis flowmeter is expected to be used in a wide range of fields.
FIGS. 7(a)-(b) shows the typical structure and operating principle of a Coriolis type mass flowmeter that has conventionally been put into practical use. Reference numeral 1 indicates a U-shaped tube through which a fluid flows and which has at its center, indicated by reference numeral 2, an excitation electromagnetic coil. The U-shaped tube is caused to make a fine rotational vibration (forced vibration) in a direction ø or in a direction −ø. The fluid flows through the U-shaped tube in the direction as indicated by an arrow v in the figure. Since the respective flow directions in the right-hand and left-hand pipe portions are opposite to each other, the Coriolis force is exerted to twist the U-shaped tube.
When the rotating direction is −ø, a torsional torque is exerted in the opposite direction. When there is no flow, the U-shaped tube makes a parallel vibration, whereas, when there is a flow, a torsional vibration in a direction θ (Coriolis vibration direction) is generated in the U-shaped tube in a magnitude in proportion to the mass flow rate, with the U-shaped tube vibrating in the ±ø directions. The torsion amount is detected as a vibration phase difference at positions 3 and 4 to obtain the mass flow rate.
More specifically, a Coriolis flowmeter as shown, for example, in FIG. 8, is used. In the Coriolis flowmeter shown, the proximal end portions of a U-shaped tube 41 are supported by a wall member 42, with the fluid flowing from an inlet 43 toward an outlet 44. A support plate 46 is fixed to the forward end of the U-shaped tube 41, and a permanent magnet 47 is fixed to the lower surface of the support plate 46 to be directed downwards. The permanent magnet 47 is magnetized in the vertical direction as seen in the figure. On a base 48, there is arranged an electromagnetic coil 49 to face the lower end surface of the permanent magnet 47. By supplying positive and negative electric currents alternately to the electromagnetic coil 49, the forward end portion of the U-shaped tube 41 is vibrated.
Permanent magnets 52 and 53 are respectively fixed to the outer side surfaces of straight pipe portions 50 and 51 on either side of the U-shaped tube 41, and a pick-up 55 formed of a coil is arranged on a support plate 54 fixed to the base 48 to be opposed to the side end surface of the permanent magnet 52. Similarly, a pick-up 57 similar to the pick-up 55 is arranged on a support plate 56 fixed to the base 48.
In the above-described device, when the electromagnetic coil 49 is operated, and a curved pipe portion 45 is moved downwards as stated above, with a fluid flowing through the U-shaped tube 41, a fine rotation is generated in the U-shaped tube 41 due to the operating principle of the Coriolis flowmeter. Since the fluid is flowing through the U-shaped tube in the direction indicated by the arrows, the flow directions in the right-hand and left-hand pipe portions are opposite to each other, and there are generated a downward force as seen in the figure in the straight pipe portion 50 and an upward force as seen in the figure in the straight pipe portion 51 as Coriolis forces. Conversely, when the curved tube portion 45 is moved upwards, an upward force is generated in the straight pipe portion 50, and a downward force is generated in the straight pipe portion 51. Thus, the Coriolis forces are exerted to twist the U-shaped tube.
Due to the above action, the U-shaped tube 41 makes movements as shown, for example, in FIGS. 9(a)-(c). The right-hand and left-hand straight pipe portions, in particular, make movements as shown in the schematic operation diagram of FIG. 10(a). That is, with the fluid flowing through the U-shaped tube 41 as stated above, the forward end of the tube is moved up and down. As shown, for example, in the left-hand column of FIG. 10(a), when the curved tube portion at the forward end of the U-shaped tube moves downwards as indicated by an open arrow, the left-hand straight pipe portion 51 lags behind the right-hand straight pipe portion 50 in its downward movement since a downward force is generated in the right-hand straight pipe portion 50 as seen in the figure, whereas an upward force is generated in the left-hand straight pipe portion 51. Conversely, as shown in the right-hand column of the figure, when the forward end portion of the U-shaped tube moves upwards, the left-hand straight pipe portion 51 lags behind the right-hand straight pipe portion 50 in its upward movement since an upward force is generated in the straight pipe portion 50 on the right-hand side as seen in the figure, whereas a downward force is generated in the straight pipe portion 51 on the left-hand side. From this onward, operations as described above are repeatedly effected.
Since the straight pipe portions make the above-described relative movements as a result of the vibration of the curved tube portion 45 at the forward end of the U-shaped tube 41, the permanent magnets 52 and 53 provided on the straight pipe portions as shown in FIGS. 8 and 9 also make similar movements. As a result, the detection signals from the right-hand and left-hand pick-ups 55 and 57 for detecting the above movements are signals having a phase difference as shown in FIG. 10(b). The higher the mass flow rate of the fluid flowing through the tube, the larger the phase difference time τ, so the mass flow rate is measured by detecting this phase difference time.
In an actual device, the pipe diameter ranges from 1.5 mm to 600 mm, and the flow rate range is 0 kg/h to 680,000 kg/h. In the case of density measurement, the measurement range is 0 kg/m3 to 3,000 kg/m3. The range of temperature at which the actual device is used is from −240° C. to 204° C. The range of pressure under which the actual device is used is from 0.12 MPa to 39.3 MPa, and the weight of the measurement device ranges from 8 kg to 635 kg. As the material of the main portions, there is used stainless steel, hastelloy C, titanium, zirconium or the like. In such a Coriolis flowmeter, the angle by which the U-shaped tube is twisted is 0.01 degrees or less.
In the above-described conventional Coriolis flowmeter using a U-shaped tube, the torsion amount of the U-shaped tube is measured as phase difference time, thereby making it possible to measure mass flow rate with very high accuracy. This is an advantage over the Coriolis flowmeters and the gyroscopic mass flowmeters of the year 1980 or earlier.
An examination of such a Coriolis flowmeter from the viewpoint, in particular, of an improvement in sensitivity, reveals the following fact. That is, using the phase difference time τ, a theoretical equation for calculating mass flow rate Qm by the above Coriolis flowmeter is expressed as follows:
                    [                  Equation          ⁢                                          ⁢          1                ]                                                            Qm        =                                                            K                θ                            ⁡                              (                                  1                  -                                                            ω                      ϕ                      2                                        /                                          ω                      θ                      2                                                                      )                                                    2              ⁢                              d                2                                              ·          τ                                    (        1        )            where Qm is the mass flow rate, Kθ is the spring constant in the twisting direction (direction θ) due to a Coriolis force, ωθ is the natural frequency (Coriolis natural frequency) in the same direction, ω526  is the natural frequency (drive frequency) in the direction of the forced vibration (direction ø), d is the distance between the parallel pipes, and τ is the phase difference time as obtained between the signals from the two pick-ups (which, in this case, are situated at the positions 3 and 4 of FIG. 7(a)). While in a stricter expression, the tangent function of τ is used, an approximate expression is adopted here since the value of τ is very small.
The main conventional Coriolis flowmeters, which perform measurement based on time as stated above, have enjoyed success as flowmeters of very high accuracy. Regarding time resolution, a digital signal processing, etc. utilizing a DSP or the like is also used, and it is to be assumed that, regarding time accuracy, a stage has been reached where no further substantial improvement is to be expected. However, no particularly remarkable improvement has beenmade regarding sensitivity (more precisely, the sensitivity coefficient of the phase difference time with respect to the flow rate).
When considered in terms of an improvement in sensitivity, equation (1) reveals the fact that, if Qm remains the same, τ increases when the coefficients other than τ are made as small as possible. Re-arranging equation (1) using τ and the frequency ratio α=(drive frequency ω526/Coriolis frequency ω74), the following equation (2) is derived. In FIGS. 11(a)-(b), the horizontal axis indicates the frequency ratio α.
                    [                  Equation          ⁢                                          ⁢          2                ]                                                            τ        =                                            2              ⁢                              Q                m                            ⁢                              d                2                                                                    K                θ                            ⁡                              (                                  1                  -                                                            ω                      ϕ                      2                                        /                                          ω                      θ                      2                                                                      )                                              =                                                    2                ⁢                                  Q                  m                                ⁢                                  d                  2                                                                              K                  θ                                ⁡                                  (                                      1                    -                                          α                      2                                                        )                                                      ⁢                                                            ,                                                                      (                                          α                      =                                                                        ω                          ϕ                                                                          ω                          θ                                                                                      )                                                                                                          (        2        )            In the graph, 2Qmd2/Kθ, which is a Y-intercept, is 1. The graph includes a curve indicating the sensitivity when there is viscosity attenuation in the vibration system. Symbol λ indicates the attenuation ratio due to viscosity. In an ordinary Coriolis flowmeter, the damping ratio is very small if not zero.
Thus, in designing a flowmeter of a satisfactory performance, it matters how the value of 2Qmd2/Kθ is to be increased and how the value of the frequency ratio α is determined to attain good characteristics.
From the above, for an improved frequency, the following measures may be taken:
(1) To bring the value of α, which is the natural frequency ratio, close to 1 to enhance the sensitivity.
(2) To make the width d as large as possible.
(3) To reduce Kθ, which is a torsion spring constant. (That is, the twisting is made easier to effect).
Regarding Coriolis flowmeters, the following documents are available.                [Patent Document 1] JP 2704768 B        [Patent Document 2] JP 58-117416 A        [Patent Document 3] JP 54-4168 A        